Polytope of Type {2,2,4,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {2,2,4,6,10}
Number of vertices, edges, etc : 2, 2, 4, 12, 30, 10
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {2,2,4,6,2}*384c
10-fold quotients : {2,2,4,3,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)
( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)
( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)
( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)
( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)
( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)
(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)
(117,119)(118,120)(121,123)(122,124);;
s3 := ( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 25, 45)( 26, 47)( 27, 46)
( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)
( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 41, 61)( 42, 63)( 43, 62)
( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 85,105)( 86,107)
( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)
( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120)(101,121)(102,123)
(103,122)(104,124);;
s4 := ( 5, 45)( 6, 48)( 7, 47)( 8, 46)( 9, 61)( 10, 64)( 11, 63)( 12, 62)
( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 53)( 18, 56)( 19, 55)( 20, 54)
( 21, 49)( 22, 52)( 23, 51)( 24, 50)( 26, 28)( 29, 41)( 30, 44)( 31, 43)
( 32, 42)( 33, 37)( 34, 40)( 35, 39)( 36, 38)( 65,105)( 66,108)( 67,107)
( 68,106)( 69,121)( 70,124)( 71,123)( 72,122)( 73,117)( 74,120)( 75,119)
( 76,118)( 77,113)( 78,116)( 79,115)( 80,114)( 81,109)( 82,112)( 83,111)
( 84,110)( 86, 88)( 89,101)( 90,104)( 91,103)( 92,102)( 93, 97)( 94,100)
( 95, 99)( 96, 98);;
s5 := ( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 65)( 10, 66)( 11, 67)( 12, 68)
( 13, 81)( 14, 82)( 15, 83)( 16, 84)( 17, 77)( 18, 78)( 19, 79)( 20, 80)
( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 89)( 26, 90)( 27, 91)( 28, 92)
( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33,101)( 34,102)( 35,103)( 36,104)
( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41, 93)( 42, 94)( 43, 95)( 44, 96)
( 45,109)( 46,110)( 47,111)( 48,112)( 49,105)( 50,106)( 51,107)( 52,108)
( 53,121)( 54,122)( 55,123)( 56,124)( 57,117)( 58,118)( 59,119)( 60,120)
( 61,113)( 62,114)( 63,115)( 64,116);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)
( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)
( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)
( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)
( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)
( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)
( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)
(114,116)(117,119)(118,120)(121,123)(122,124);
s3 := Sym(124)!( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 22, 23)( 25, 45)( 26, 47)
( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)( 32, 52)( 33, 53)( 34, 55)
( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)( 40, 60)( 41, 61)( 42, 63)
( 43, 62)( 44, 64)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 82, 83)( 85,105)
( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)( 91,110)( 92,112)( 93,113)
( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)( 99,118)(100,120)(101,121)
(102,123)(103,122)(104,124);
s4 := Sym(124)!( 5, 45)( 6, 48)( 7, 47)( 8, 46)( 9, 61)( 10, 64)( 11, 63)
( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 53)( 18, 56)( 19, 55)
( 20, 54)( 21, 49)( 22, 52)( 23, 51)( 24, 50)( 26, 28)( 29, 41)( 30, 44)
( 31, 43)( 32, 42)( 33, 37)( 34, 40)( 35, 39)( 36, 38)( 65,105)( 66,108)
( 67,107)( 68,106)( 69,121)( 70,124)( 71,123)( 72,122)( 73,117)( 74,120)
( 75,119)( 76,118)( 77,113)( 78,116)( 79,115)( 80,114)( 81,109)( 82,112)
( 83,111)( 84,110)( 86, 88)( 89,101)( 90,104)( 91,103)( 92,102)( 93, 97)
( 94,100)( 95, 99)( 96, 98);
s5 := Sym(124)!( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 65)( 10, 66)( 11, 67)
( 12, 68)( 13, 81)( 14, 82)( 15, 83)( 16, 84)( 17, 77)( 18, 78)( 19, 79)
( 20, 80)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 89)( 26, 90)( 27, 91)
( 28, 92)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33,101)( 34,102)( 35,103)
( 36,104)( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41, 93)( 42, 94)( 43, 95)
( 44, 96)( 45,109)( 46,110)( 47,111)( 48,112)( 49,105)( 50,106)( 51,107)
( 52,108)( 53,121)( 54,122)( 55,123)( 56,124)( 57,117)( 58,118)( 59,119)
( 60,120)( 61,113)( 62,114)( 63,115)( 64,116);
poly := sub<Sym(124)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope